Finite Frequency Filtering Design for Uncertain Discrete-Time Systems Using Past Output Measurements

This paper tackles the problem of finite frequency
$\mathcal H_{\infty }$
filtering design for polytopic uncertain discrete-time systems using past output measurements. The noise is assumed to be restricted in a finite frequency range, i.e., the low, middle, or high frequency range. The objective is to design an admissible filter with past output measurements of the system, guaranteeing the asymptotic stability of the filtering error system with a prescribed finite frequency
$\mathcal H_{\infty }$
disturbance attenuation level. Based on past output measurements together with the parameter-dependent Lyapunov function and projection lemma, a new sufficient condition for robust finite frequency
$\mathcal H_{\infty }$
performance is first derived, and then, the filter synthesis is developed. It is shown that the filter gains can be obtained by solving a set of linear-matrix-inequalities. Finally, two examples are given to demonstrate the advantages and effectiveness of the proposed approach.